let

x = the present age of chris

y = the present age of cathy

chris is six years older than cathy:

x = 6 + y

in two years, chris will be twice as old as cathy:

x + 2 = 2(y + 2)

by solving the system of equations:

x = 6 + y

x + 2 = 2(y + 2)

we find:

x = 10 years

y = 4 years

click here to see the step by step solution of the system of equations:

Chris is 10 years old now.

Cathy is 4 years old now.